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Numerical problems on ratio analysis

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Unit 3:
Ratio Analysis
Meaning:
A ratio is a mathematical number calculated as a reference to relationship of two or
more numbers and can be expressed as a fraction, proportion, percentage and a
number of times. When the number is calculated by referring to two accounting
numbers derived from the financial statements, it is termed as accounting ratio.
It needs to be observed that accounting ratios exhibit relationship, if any, between
accounting numbers extracted from financial statements. Ratios are essentially derived
numbers and their efficacy depends a great deal upon the basic numbers from which
they are calculated.
Further, a ratio must be calculated using numbers which are meaningfully correlated.
Objectives of Ratio Analysis:
Ratio analysis is indispensable part of interpretation of results revealed by the financial
statements. It provides users with crucial financial information and points out the
areas which require investigation. Ratio analysis is a technique which involves
regrouping of data by application of arithmetical relationships, though its
interpretation is a complex matter. It requires a fine understanding of the way and the
rules used for preparing financial statements. Once done effectively, it provides a lot of
information which helps the analyst:
1. To know the areas of the business which need more attention;
2. To know about the potential areas which can be improved with the effort in the
desired direction;
3. To provide a deeper analysis of the profitability, liquidity, solvency and efficiency
levels in the business;
4. To provide information for making cross-sectional analysis by comparing the
performance with the best industry standards; and
5. To provide information derived from financial statements useful for making
projections and estimates for the future.
Importance (or Advantages) of Ratio Analysis:
1. Helps to understand efficacy of decisions: The ratio analysis helps you to
understand whether the business firm has taken the right kind of operating,
investing and financing decisions. It indicates how far they have helped in
improving the performance.
2. Simplify complex figures and establish relationships: Ratios help in simplifying
the complex accounting figures and bring out their relationships. They help
summarise the financial information effectively and assess the managerial
efficiency, firm’s credit worthiness, earning capacity, etc.
3. Helpful in comparative analysis: The ratios are not be calculated for one year
only. When many year figures are kept side by side, they help a great deal in
exploring the trends visible in the business. The knowledge of trend helps in making
projections about the business which is a very useful feature.
4. Identification of problem areas: Ratios help business in identifying the problem
areas as well as the bright areas of the business. Problem areas would need more
attention and bright areas will need polishing to have still better results.
5. Enables SWOT analysis: Ratios help a great deal in explaining the changes
occurring in the business. The information of change helps the management a great
deal in understanding the current threats and opportunities and allows business to
do its own SWOT (Strength-Weakness-Opportunity-Threat) analysis.
6. Various comparisons: Ratios help comparisons with certain bench marks to
assess as to whether firm’s performance is better or otherwise. For this purpose, the
profitability, liquidity, solvency, etc. of a business, may be compared: (i) over a
number of accounting periods with itself (Intra-firm Comparison/Time Series
Analysis), (ii) with other business enterprises (Inter-firm Comparison/Crosssectional Analysis) and (iii) with standards set for that firm/industry (comparison
with standard (or industry expectations).
Limitations of Ratio Analysis:
1. Limitations of Accounting Data: Accounting data give an unwarranted
impression of precision and finality. In fact, accounting data “reflect a combination
of recorded facts, accounting conventions and personal judgements which affect
them materially. For example, profit of the business is not a precise and final figure.
It is merely an opinion of the accountant based on application of accounting
policies. The soundness of the judgement necessarily depends on the competence
and integrity of those who make them and on their adherence to Generally Accepted
Accounting Principles and Conventions”. Thus, the financial statements may not
reveal the true state of affairs of the enterprises and so the ratios will also not give
the true picture.
2. Ignores Price-level Changes: The financial accounting is based on stable money
measurement principle. It implicitly assumes that price level changes are either
non-existent or minimal. But the truth is otherwise. We are normally living in
inflationary economies where the power of money declines constantly. A change in
the price-level makes analysis of financial statement of different accounting years
meaningless because accounting records ignore changes in value of money.
3. Ignore Qualitative Aspects: Accounting provides information about quantitative
(or monetary) aspects of business. But sometimes qualitative factors may surmount
the quantitative aspects. The calculations derived from the ratio analysis under
such circumstances may get distorted. For E.g., though credit may be granted to a
customer on the basis of information regarding his financial position, yet the grant
of credit ultimately depends on debtor’s character, honesty, past record and his
managerial ability.
4. Variations in Accounting Practices: There are differing accounting policies for
valuation of inventory, calculation of depreciation, treatment of intangibles Assets
definition of certain financial variables etc., available for various aspects of business
transactions. These variations leave a big question mark on the cross-sectional
analysis. As there are variations in accounting practices followed by different
business enterprises, a valid comparison of their financial statements is not
possible.
5. Forecasting: Forecasting of future trends based only on historical analysis is not
feasible. Proper forecasting requires consideration of non-financial factors as well.
6. Lack of ability to resolve problems: Their role is essentially indicative and of
whistle blowing and not providing a solution to the problem.
Balance Sheet Ratios:
1. Current Ratio = Current Assets
Current Liabilities
2. Liquid Ratio =
•
•
Quick (Liquid) Assets
Quick (Liquid) Liabilities
Liquid assets are those which are readily converted into cash and will
include cash/ bank balances, bills receivable, sundry debtors and short term
investments. Inventories and Prepaid Expenses are not included in
liquid assets.
Liquid Liabilities includes all items of current liabilities except Bank
Overdraft.
3. Proprietary Ratio = Proprietors funds
Total Assets
•
•
Proprietor fund = Share capital(Equity & Pref.) + Retained earnings (less loss if
any) -Fictitious assets
Total Assets = Fixed Assets + Current Assets-Fictitious assets
4. Stock Working capital Ratio = Closing Stock
Working Capital
•
Working Capital = Current assets – Current liabilities
5. Capital Gearing Ratio = Fixed Interest & Dividend Bearing Funds
Equity Share holders fund
•
Equity Share holders fund= Equity Sh. Capital + Retained earnings (less loss if
any) -Fictitious assets
6. Debt Equity Ratio =
Long Term Debt
Proprietors Fund
Prob1:
Liabilities
Equity Share Capital
Preference share capital
General Reserve
Secured Loan
Sundry Creditors
Rs.
5,00,000
2,00,000
1,00,000
3,00,000
1,00,000
Assets
Land & Building
Machinery
Furniture
Inventory
Sundry Debtors
Cash/Bank Balance
12,00,000
Calculate Following Ratios from the above balance sheet:
1. Current Ratio
2. Liquid Ratio
Rs.
1,00,000
4,00,000
50,000
3,00,000
3,00,000
50,000
12,00,000
3. Proprietary Ratio
4. Stock Working capital Ratio
5. Capital Gearing Ratio
6. Debt Equity Ratio
Solution:
1. Current ratio
= Current assets/current liabilities
Current
assets
=
inventory
(3,00,000)+
s.debtors(3,00,000) + cash balance(50,000) = 6,50,000
Current liabilities = S.Creditors = 1,00,000
2. Liquid ratio
= 6,50,000/1,00,000
= 6.5:1
= liquid assets/liquid liabilities
liquid assets = s.debtors(3,00,000) + cash balance(50,000)
= 3,50,000
liquid liabilities = S.Creditors = 1,00,000
3. Proprietary Ratio
= 3,50,000/1,00,000
= 3.5:1
Proprietors fund / total assets
Proprietor fund = Share capital(Equity & Pref.) + Retained
earnings (less loss if any) -Fictitious assets
= 5,00,000 + 2,00,000 + 100,000 = 8,00,000
Total Assets = Fixed Assets + Current Assets-Fictitious
assets
= 12,00,000
4. Stock
Working
capital Ratio
5. Capital
Ratio
Gearing
= 800,000/12,00,000
= 0.66 : 1
= closing stock / working capital
= 300,000 / 5,50,000
= 0.55:1
Working capital (CA-CL= 6,50,000 – 1,00,000 = 5,50,000)
= Fixed Interest & Dividend Bearing Funds
Equity Share holders fund
Fixed Interest & Dividend Bearing Funds = pref sh.
(2,00,000) + secured loan (3,00,000) = 500,000
Equity Share holders fund = Eq. Shares (5,00,000) + GR
(100,000) = 600,000
6. Debt
Ratio
Equity
= 500,000 / 600,000
= 0.83 : 1
=Long Term Debt
Proprietors Fund
Long term debt = secured loan (300,000)
= 3,00,000/8,00,000
= 0.38 : 1
Prob 2:
Liabilities
Equity Share Capital
12% Preference share capital
General Reserve
16% debentures
Trade payable
Bank overdraft
Provision for Income Tax
Rs.
Assets
Rs.
2,00,000 Machinery
5,92,000
3,60,000 Investment
2,24,000
1,40,000 Stock
2,02,000
2,40,000 Bills Receivable
40,000
2,44,000 S. Debtors
98,000
40,000 Cash and Bank
76,000
36,000 Profit & Loss A/c
28,000
12,60,000
12,60,000
Calculate Following Ratios from the above balance sheet:
1. Current Ratio
2. Liquid Ratio
3. Proprietary Ratio
4. Capital Gearing Ratio
5. Debt Equity Ratio
Solution:
1. Current ratio
= Current assets/current liabilities
Current assets = stock (2,02,000)+ BR (40,000)+
s.debtors(98000) + cash balance(76,000) = 4,16,000
Current liabilities = trade payable (2,44,000) + Bank
o/d(40,000) + provision for income tax (36,000) = 320,000
2. Liquid ratio
= 4,16,000/3,20,000
= 1.3:1
= liquid assets/liquid liabilities
liquid assets = BR (40,000)+ s.debtors(98000) + cash
balance(76,000) = 2,14,000
liquid liabilities = trade payable (2,44,000) provision for
income tax (36,000) = 2,80,000
3. Proprietary Ratio
= 2,14,000/2,80,000
= 0.76:1
Proprietors fund / total assets
Proprietor fund = Share capital(Equity & Pref.) + Retained
earnings (less loss if any) -Fictitious assets
= 2,00,000 + 3,60,000 + 140,000-28,000 = 6,72,000
Total Assets = Fixed Assets + Current Assets-Fictitious
assets
= 12,60,000 – 28,000 = 12,32,000
4. Capital
Ratio
Gearing
= 6,72,000/12,32,000
= 0.55 : 1
= Fixed Interest & Dividend Bearing Funds
Equity Share holders fund
Fixed Interest & Dividend Bearing Funds = pref sh.
(3,60,000) + debentures (2,40,000) = 6,00,000
Equity Share holders fund = Eq. Shares (2,00,000) + GR
(1,40,000) – profit & loss (28000) = 3,12,000
5. Debt
Ratio
Equity
= 600,000 / 3,12,000
= 1.92 : 1
=Long Term Debt
Proprietors Fund
Long term debt = debentures (2,40,000)
= 2,40,000/6,70,000
= 0.36 : 1
Practice problems:
Prob 3:
Liabilities
Equity Share Capital
10% Preference share capital
General Reserve
15% debentures
Trade payable
Bank overdraft
Provision for Tax
Rs.
Assets
1,00,000 Furniture
1,80,000 Trademarks
70,000 Stock
1,20,000 Bills Receivable
1,22,000 Trade Receivables
20,000 Cash and Bank
18,000 Profit & Loss A/c
6,30,000
Calculate Following Ratios from the above balance sheet:
1. Current Ratio
2. Liquid Ratio
3. Proprietary Ratio
4. Capital Gearing Ratio
5. Debt Equity Ratio
Rs.
2,96,000
1,12,000
1,01,000
20,000
49,000
38,000
14,000
6,30,000
Prob 4:
The Balance Sheet of Trident Limited as on 31‐12‐2017 was as follow:
Liabilities
Equity Share Capital
Capital Reserve
Profit & Loss A/c
7% Mortgage Loan
Creditors
Bank overdraft
Provision for Income Tax
Rs.
Assets
40,000 Plant & Machinery
8,000 Land & Building
12,000 Furniture & Fixtures
32,000 Stock
16,000 Debtors
4,000 Investment (Short-term)
8,000 Cash at bank
1,20,000
You are required to Calculate Following Ratios:
1. Current Ratio (1.43:1)
2. Liquid Ratio (1.17:1)
3. Proprietary Ratio (0.5: 1) or 50%)
4. Capital Gearing Ratio (0.53: 1)
5. Debt Equity Ratio (0.53: 1) or 53%)
Rs.
24,000
40,000
16,000
12,000
12,000
4,000
12,000
1,20,000
Prob 5:
The Balance Sheet of omega Limited as on 31‐12‐2018 was as follow:
Liabilities
Equity Share Capital
8% Pref. Share Capital
Reserves & Surplus
10% Debenture
9% Secured Loan
Creditors
Bank overdraft
Bills Payable
Outstanding Expenses
Rs.
Assets
20,00,000 Machinery
15,00,000 Patents & Trademarks
11,00,000 Stock
10,00,000 Debtors
5,00,000 Bills Receivables
1,00,000 Cash at bank
1,50,000 Fictitious Assets
45,000
5,000
64,00,000
You are required to Calculate Following Ratios:
1. Current Ratio (2.67:1)
2. Liquid Ratio (4.17:1)
3. Proprietary Ratio (0.71: 1) or 71%)
4. Capital Gearing Ratio (1: 1)
5. Debt Equity Ratio (0.33: 1) or 33%)
Prob 6:
Following is the summarised Balance Sheet of Borkar tiles Ltd. as on 31‐3‐19.
Liabilities
Rs.
Assets
Equity Shares of Rs. 10 Each
10,00,000 Fixed Assets
10% Pref. Shares of Rs. 100
4,00,000 Investments
each
Closing Stock
Reserves and surplus
7,00,000 S. Debtors
15% Debentures
5,00,000 Bills Receivables
Sundry Creditors
2,40,000 Cash Balance
Bank Overdraft
1,60,000 Preliminary Expenses
30,00,000
You are required to Calculate Following Ratios:
1. Current Ratio (1.95:1)
2. Liquid Ratio (2.42:1)
3. Proprietary Ratio (0.70: 1) or 70%)
4. Capital Gearing Ratio (0.54: 1)
5. Debt Equity Ratio (0.24: 1) or 24%)
Rs.
35,00,000
20,00,000
1,75,000
3,50,000
50,000
2,25,000
1,00,000
64,00,000
Rs.
20,00,000
2,00,000
2,00,000
4,60,000
60,000
60,000
20,000
30,00,000
INCOME STATEMENT RATIOS:
1. Gross Profit Ratio = Gross Profit X100
Net Sales
Purpose: Indicates the efficiency of production and trading operations
.
2. Operating Ratio = Cost of Goods Sold + Operating Expenses X100
Net Sales
Purpose: index of managerial ability to control operating expenses.
3. Expenses Ratio= Operating Expenses X100
Net Sales
(Expenditure may be cost of production or Cost of sales, administrative or Selling or
distribution expenses or any other Element of Group)
Purpose: Indicates the direction in which economies ought to be effected.
4. Net Operating Profit Ratio = Operating Profit X100
Net Sales
Purpose: Index of Operating Efficiency.
5. Net Profit Ratio = Net Profit After Tax X100
Net Sales
Purpose: Indicates Net Margin on sales.
Prob. 1:
Following is the Income Statement of Urja Auto. Ltd. For the year ended 31st Dec 2019. You
are required to calculate: 1) Gross Profit Ratio; 2) Operating Ratio; 3) Net operating Profit
Ratio and 4) Net Profit Ratio.
Particulars
Sales
Less: Cost of goods Sold
Gross Profit
Less: Operating Expenses
Operating Profit
Add: Non –operating income
Less: Non –operating Expenses
Profit before Tax
Less: Tax @ 30%
Net Profit After Tax
Rs.
20,00,000
12,00,000
8,00,000
4,80,000
3,20,000
48,000
3,68,000
16,000
3,52,000
1,05,600
2,46,400
Solution: (Hint: only needs to replace available figures with respective formula to arrive at
answer)
1. Gross Profit Ratio = 800000/20,00,000 x 100 = 40%
2. Operating ratio = 12,00,000 + 4,80,000 X100 = 84%
20,00,000
3. Net operating profit Ratio = 3,20,000/20,00,000 x 100 = 16%
4. Net profit ratio = 2,46,400/20,00,000 x 100 = 12.3%
Prob. 2:
The following Trading and Profit and Loss Account of Tiptop Ltd. for the year 31‐3‐2019 is given
below:
Particulars
To opening stock
To purchases
To Carriage inward
To wages
To Gross profit c/f
Rs.
Particulars
76,250 By Sales
3,15,250 By Closing stock
2,000
5,000
2,00,000
5,98,500
To
Administrative 1,01,000 By Gross profit b/d
exp.
12,000 By interest on securities
To Selling & dist.
2,000 By dividend on shares
7,000 By profit on sale of
Exp.
To non operating
84,000 shares
exp.
To financial exp.
To net profit c/d
2,06,000
Calculate: Gross profit ratio, Expense ratio, operating ratio,
profit ratio.
Solution:
1. Gross profit ratio = 2,00,000/500,000 x 100 = 40%
Rs.
5,00,000
98,500
5,98,500
2,00,000
1,500
3,750
750
2,06,000
net operating profit ratio & net
2. Expense ratio = operating exp. / net sales x 100
1,13,000+5,00,000 x 100 = 22.60%
3. Operating ratio = cost of goods sold +operating Exp / net sales x100
3,00,000 + 1,13,000 x100
5,00,000
(Cost of Goods sold = Op. stock + purchases + carriage inward + wages – Closing Stock)
4. Operating profit ratio = operating profit / net sales
= 87,000 /5,00,000 x 100 = 17.40%
(Operating profit = sales – (cost of goods sold + operating exp.)
5. Net profit ratio = Net profit/net sales x 100
84,000 / 5,00,000 x 100 = 16.8%
Practice problems:
Prob. 3:
Following is the Income Statement of Durv Pvt. Ltd. For the year ended 31st March 2017.
Particulars
Net Sales
Less: Cost of goods Sold
Gross Profit
Less: Operating Expenses
Operating Profit
Add: Non –operating income
Less: Non –operating Expenses
Profit before Tax
Tax Rate is 40%
Rs.
12,00,000
7,00,000
5,00,000
2,00,000
3,00,000
45,000
3,45,000
25,000
3,20,000
Calculate: 1) Gross Profit Ratio; 2) Operating Ratio; 3) Net operating Profit Ratio and 4) Net
Profit Ratio.
Prob. 4:
From the following information for the year ended 31st Dec 2018, You are required to
calculate: 1) Gross Profit Ratio; 2) Operating Ratio; 3) Net operating Profit Ratio and 4) Net
Profit Ratio.
Total Sales- Rs. 5,00,000/Sales Return- Rs. 50,000/Gross Profit – 40% of Net Sales.
Cost of goods sold – Rs. ??
Operating Expenses – Rs.60,000/Non-operating Income – Rs. 21,000/Tax Rate is 50%
Hint: first prepare income statement and then calculate ratios.
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